Local mesh operators: extrusions revisited

In this paper, we present a set of generalized "local" mesh operators. Local operators are those that operate on a single face without affecting the rest of the mesh. Boundary edges of the chosen face also stay the same. We have identified two types of local operators: (1) Extrusions that create generalized pipes in which bottom and top polygons have the same number of sides, and (2) Stellations that create generalized pyramids, where there is a top vertex instead of top polygon. Our operators can create extrusions that are regular polyhedra including dodecahedron, icosa-hedron, octahedron and tetrahedron. The tetrahedron is created using the stellation operator, which is also useful to create generalized versions of Kepler and Poinsot solids.